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Paper details
Number 2 - June 2015
Volume 25 - 2015
A fuzzy nonparametric Shewhart chart based on the bootstrap approach
Dabuxilatu Wang, Olgierd Hryniewicz
Abstract
In this paper, we consider a nonparametric Shewhart chart for fuzzy data. We utilize the fuzzy data without transforming
them into a real-valued scalar (a representative value). Usually fuzzy data (described by fuzzy random variables) do not have
a distributional model available, and also the size of the fuzzy sample data is small. Based on the bootstrap methodology,
we design a nonparametric Shewhart control chart in the space of fuzzy random variables equipped with some L2 metric, in which a novel approach for generating the control limits is proposed. The control limits are determined by the necessity index of strict dominance combined with the bootstrap quantile of the test statistic. An in-control bootstrap ARL of the proposed chart is also considered.
Keywords
Shewhart control chart, fuzzy data, bootstrap, average run length